This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133661 #7 May 18 2019 10:58:11
%S A133661 1,8,25,86,209,472,25719,238350,41931245,14426603100
%N A133661 No sum of 2 or more terms equals a prime, terms alternate parity and there are no primes in the list.
%C A133661 a(10) > 263811880. - _Robert G. Wilson v_, Jan 01 2008
%e A133661 25 is a term, because 25 is odd (previous term was even), 25 is composite and 25+1, 25+8 and 25+8+1 are all composite.
%t A133661 (* first do *) Needs["Combinatorica`"] (* then *) lst = {1, 8}; g[k_] := Block[{j = 1, l = 2^Length@lst}, While[j < l && !PrimeQ[Plus @@ NthSubset[j, lst] + k], j++ ]; If[j == l, False, True]]; f[n_] := Block[{k = lst[[ -1]] + 1}, While[PrimeQ@k || g[k] == True, k++; k++ ]; AppendTo[lst, k]; k]; Do[ Print@ f@ n, {n, 10}] (* _Robert G. Wilson v_, Jan 01 2008 *)
%Y A133661 Cf. A052349, A133660.
%K A133661 more,nonn
%O A133661 1,2
%A A133661 _Randy L. Ekl_, Dec 28 2007
%E A133661 a(9) from _Robert G. Wilson v_, Jan 01 2008
%E A133661 a(10) from _Donovan Johnson_, Feb 15 2008